Is it legislated to say "Prayer is better than sleep" in the Fajr Adhan for someone who missed the prayer and woke up late, and should his prayer be audible or silent?

For an individual, the Adhan (call to prayer) is a confirmed Sunnah (Prophet's tradition). It is prescribed to be performed for a missed prayer. It should be complete with all its phrases, including "Prayer is better than sleep" in the Fajr Adhan. It is also sunnah for an individual to recite aloud during the Fajr prayer and the first two rak'ahs of Maghrib and Isha prayers.